Solve the system for x and y using Cramerʹs rule. Assume a and b are nonzero constants.
-$$x + a y = \frac { 1 } { a }$$
$$x + b y = \frac { 1 } { b }$$
A) $\left\{ \left( b + a , - \frac { 1 } { a b } \right) \right\}$
B) $\left\{ \left( \frac { \mathrm { b } - \mathrm { a } } { \mathrm { ab } } , - \frac { 1 } { \mathrm { ab } } \right) \right\}$
C) $\left\{ \left( \frac { a + b } { a b } , - \frac { 1 } { a b } \right) \right\}$
D) $\left\{ \left( \frac { 1 } { a b } , \frac { a - b } { a b } \right) \right\}$

Question

Quizplus · Accepted Answer

Cramer's rule uses determinants to solve a system of linear equations. For the given system, the determinant of the coefficient matrix and the determinants of the matrices with the constants substituted into the respective columns are calculated. The solution for $x$ and $y$ using Cramer's rule results in $x = \frac{a+b}{ab}$ and $y = -\frac{1}{ab}$, which matches choice C.

Solve the System for X and Y Using Cramerʹs Rule x+ay=1ax + a y = \frac { 1 } { a }x+ay=a1​

Solve the System for X and Y Using Cramerʹs Rule $x + a y = \frac { 1 } { a }$